Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.21037 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910062779301888 |
|---|---|
| author | Lin, Yiran Markovic, Vladimir |
| author_facet | Lin, Yiran Markovic, Vladimir |
| contents | Let $S$ be an arbitrary Riemann surface whose Teichmüller space $T(S)$ has dimension at least two. A long standing problem is to determine whether the Carathéodory metric $d_C$ agrees with the Teichmüller metric $d_T$ on $T(S)$. It was shown that $d_C\ne d_T$ when $S$ is a closed surface of genus at least two. In this paper we study the general case, and prove that $d_C\ne d_T$ on $T(S)$ except possibly on the following seven Teichmüller spaces: $T^1_{0,0}$, $T^1_{0,1}$, $T^2_{0,0}$, $T^1_{0,2}$, $T^2_{0,1}$, $T^3_{0,0}$, and $T^3_{0,1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Caratheodory metrics on Teichmuller spaces Lin, Yiran Markovic, Vladimir Geometric Topology Complex Variables 20H10 Let $S$ be an arbitrary Riemann surface whose Teichmüller space $T(S)$ has dimension at least two. A long standing problem is to determine whether the Carathéodory metric $d_C$ agrees with the Teichmüller metric $d_T$ on $T(S)$. It was shown that $d_C\ne d_T$ when $S$ is a closed surface of genus at least two. In this paper we study the general case, and prove that $d_C\ne d_T$ on $T(S)$ except possibly on the following seven Teichmüller spaces: $T^1_{0,0}$, $T^1_{0,1}$, $T^2_{0,0}$, $T^1_{0,2}$, $T^2_{0,1}$, $T^3_{0,0}$, and $T^3_{0,1}$. |
| title | Caratheodory metrics on Teichmuller spaces |
| topic | Geometric Topology Complex Variables 20H10 |
| url | https://arxiv.org/abs/2603.21037 |